MOND, FUGE and Dark Matter Light

In What FUGE does not explain, I make the outrageous claim that dark matter does not exist (at least not in the FUGE model).  This is based on the fact that, in the FUGE model, the mass-energy of the universe at this time is equivalent to 8.77×10⁵²kg.

 

However, it should be noted that the amount ordinary matter in the universe is calculated, per the standard cosmological model, to be 1.46×10⁵³kg, which is higher than I arrive at.  This is because of the assumption of inflation, and the assumption of dark matter and dark energy.  The 1.5×10⁵³kg figure is based on an assumption of total energy density of 9.9×10^-27kg/m³, applied to a universe that is 46.5 billion light years in radius and multiplied by 4.8% (the proportion of ordinary matter in the standard cosmological model).  If we apply that critical density to a FUGE universe, with a radius of 13.77 billion light years, without reducing it, the figure becomes 9.17×10⁵²kg.  Note that my calculated critical density, for 13.77 billion light years, is 9.448×10^-27kg/m³, hence the 8.77×10⁵²kg figure above.

 

The complexity of this, and the outrageousness of my claim, caused me to search for any evidence that dark matter does not exist.  I found that there are indeed people who believe, for other reasons, that dark matter may not be real.  One such person is Pavel Kroupa, a professor of astrophysics at the University of Bonn and the Astronomical Institute of Charles University in Prague.  He claims that his observations falsify dark matter as a hypothesis and favours MOND, or modified Newtonian Dynamics.

 

MOND relies on an acceleration constant, a₀, which the theory’s creator (Mordehai Milgrom) worked out was about 1.2×10^-10m/s².  Basically, the theory posits that gravity works one way in high acceleration scenarios and another way in low acceleration scenarios (where a is much lower than a₀).  Unfortunately, Milgrom worked out the value via a form of numeromancy, taking the data and working out what value of a₀ would make this theory fit.

 

However, it is interesting to note that if we set a₀=c.H₀/2π, where H₀ is the inverse of the age of the universe (1/13.77 billion years = 2.301×10^-18s), we arrive at a₀=1.098×10^-10m/s².  The physical meaning of this would need to be established and note that, if it is a true relationship, then it would imply that a₀ would be a parameter that decreases with the age of the universe.  If so, then it should be possible to see hints of that in the universe today.

 

Another problem with MOND, as detailed by Milgrom himself at Scholarpedia (a location where, I discovered later, the relationship 2πa₀≈c.H₀ was identified), is that:

 

For galaxy clusters, MOND reduces greatly the observed mass discrepancy: from a factor of ∼10, required by standard dynamics, to a factor of about 2. But, this systematically remnant discrepancy is yet to be accounted for. It could be due to, e.g., the presence of some small fraction of the yet undetected, “missing baryons”, which are known to exist (unlike the bulk of the putative “dark matter”, which cannot be made of baryons).

 

Note commentary in What the FUGE model does not explain.

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And yes, I am suggesting that perhaps there *might* be some dark matter, just not as much of it as previously thought.  Call it “dark matter light”.

Note that within the MOND world, there remains a category referred to as "missing baryons" to cover a mass discrepancy, but that is not considered (by Milgrom) to be "dark matter".  However, since "dark matter" is a catch-all term to describe the phenomenon, not necessary matter per se, my pathetic little joke still works.

I should also be noted that Pavel Kroupa seems to be saying there is no dark matter whatsoever, but it's unclear whether this means there is no mass discrepancy.  I have sought clarity on that question.

What FUGE does not explain

I acknowledge that FUGE does not explain two things that contribute to the complexity of the standard cosmological model – the homogeneity/isotropy of the cosmic microwave background (at least not explicitly) and cosmic acceleration (at all).

 

The first is explained in the standard cosmological model by inflation, but there are other explanations other than inflation.  One of the authors of a Scientific American article on inflation together with Alan Guth, Paul Steinhardt, now disowns the theory, going so far as to suggest that inflationary theory “makes no testable predictions”.  The point here is not that Steinhardt’s theory (a cyclic theory of the universe) is necessarily correct either, merely that there are other ways of explaining what inflation set out to explain.

 

While it should be noted that I am not a cosmologist, I am somewhat more sanguine about homogeneity and isotropy.  If physics works the same everywhere in the universe, which seems a reasonable assumption, then if all locations began with the same conditions, in a very much localised area (relative to now), then it should not be surprising that our observations of the cosmic microwave background reveal that all parts of it have evolved over the period of 370,000 years to be pretty similar.

 

That might need a little bit of explanation.  At the beginning, for about 370,000 years, the universe was so hot that it was effectively opaque to photons.  This is known as recombination during the photon epoch – which is to say that none of the photons generated got very far before being absorbed by matter.  The cosmic microwave background is only what we can see from the time that the universe became transparent – we cannot see the Big Bang, we cannot see anything from an inflationary period, and we cannot see anything from a period of about 370,000 years after either of those.

 

Note that during those 370,000 years, the universe was a “hot dense plasma of nuclei, electrons and photons”.  It is pretty difficult to comprehend how a period of inflation of about 10^-32s that occurred 370,000 years previously would be instrumental in ensuring the level of homogeneity and isotropy that we can observe in the cosmic microwave background.  The argument already seems to incorporate the notion that physics would have operated the same way everywhere for the entirety of 370,000 years, leading the universe to evolve into a homogeneous and isotropic state.

 

Note this statement from the wikipedia entry on the photon epoch: “370,000 years after the Big Bang, the temperature of the universe fell to the point where nuclei could combine with electrons to create neutral atoms. As a result, photons no longer interacted frequently with matter, the universe became transparent and the cosmic microwave background radiation was created and then structure formation took place.”  If this is correct, and I have no reason to suspect otherwise, then once the temperature hit a certain point (apparently in the order of 10³K), neutral atoms were created and the universe became transparent.  So we should expect the entirety of the cosmic microwave background to be that temperature divided by the extent of expansion, even if the temperatures were reached at slightly different times.

 

Putting that in figures, the current cosmic microwave background temperature is 2.725K with a variation of 0.0002K between the “hot” and the “cold” regions.  Over the past 13.77 billion years (ish), the temperature has reduced by a factor of about 10³ due to the expansion of the universe (which has expanded by a factor of about 10⁴-10⁵).  The question then is: if different regions cooled down to the temperature required for neutral atoms to form at slightly different times, what effect would that have on temperature observed today?  Using the FUGE values, the universe has expanded by a factor of 3.7×10⁵ since the surface of last scattering when the cosmic microwave background was formed, assuming that it happened at precisely year 370,000 and that this is precisely year 13,770,000,000 (don’t get distracted by all the 3s and 7s, they are just an artefact of using the year as our temporal unit).

 

The standard model describes the CMB as originating from a hydrogen-helium plasma, condensing at a temperature of about 3,000K.  So, assuming this temperature to be precise, together with the 2.7250K value for the “cold” regions, the universe needed to expand by a factor of 3.76162162×10⁵ to reduce the temperature by a factor of 1.10091743×10³.  Assuming that the “hot” regions are precisely 2.7252K, how much later would they have been at 3,000K than the "cool" regions were?  It would require reduction by a factor of 1.100836636×10³, implying expansion of the universe by a factor of 3.721348495×10⁵, indicating that “hot” regions in the cosmic microwave background may have cooled down to 3,000K in the year 370,027.  So … the dappling on the cosmic radiation background that we can see could just be due to variations in the timing of the cooling of the universe by a factor of just under 30 years (or a bit under 0.01%).

 

There’s an additional assumption that can be added to the FUGE model, if one wants to explain homogeneity and isotropy, and that is that mass-energy entering the universe does so in a homogenous and isotropic manner.  This is a direct consequence of the cosmological principle (nowhere in the universe is special), so if energy is entering into or being created by the universe, then this will be happening to the same extent everywhere – similar to the notion of dark energy which involves a consistent density which implies the introduction of (mass-)energy across the universe at a rate equal to the increase in volume.

 

At year 370,000, in the FUGE model, the amount of mass-energy in the universe was equivalent to 2.356×10⁴⁸kg whereas, at 10^-36s, there was only 0.2018kg (noting that the radius at that time was 3.000×10^-28m).  This means that the vast majority of mass-energy in the universe at year 370,000 had entered after the time that, in the standard model, inflation would have commenced.  The only reason why one would consider the distribution of mass-energy at the notional time of inflationary period is that, in the standard model, there would already be 8.08×10⁵³kg of mass-energy in existence at that time.  That is simply not a factor in the FUGE model.  In other words, inflation is a solution to a problem created by the standard model.

 

Note that in the FUGE model there is, today, 8.77×10⁵²kg in the universe (so a density of 9.47×10^-27kg/m³).  The standard model has it that there is 1.5×10⁵³kg of ordinary matter, plus six times that of dark matter and more than twice that again in dark energy – in the observable universe.  This is based on the observable universe being 46.5 billion light years in radius, due to inflation.  The total amount of mass-energy in the Hubble sphere (about 14 billion light years), would be 9.17×10⁵²kg based on a density of 9.9×10^-27kg/m³.  Note that the critical density is related to the Hubble parameter which is not yet nailed down, so there is a range between 8.3×10^-27kg/m³ (Planck Collaboration) and 10.2×10^-27kg/m³ (SHOES) that my calculation comfortably falls into.

 

The standard model has the amount of ordinary matter in a Hubble sphere as 3.9×10⁵¹kg (1.5×10⁵³kg multiplied by the volume of a Hubble sphere, divided by the calculated observable universe volume [so about 2.5%]).  With the assumption that this is 4.8% of the total mass-energy, this is equivalent to 8.12×10⁵²kg in total (within the ballpark of the FUGE model estimate).  However, as the FUGE model does not distinguish between types of mass-energy, it’s worth looking at how much ordinary matter we can see using all the tools available to us (as opposed to how much can be calculated using other assumptions).

 

The observable universe contains about 10²⁴ stars (as is likely “a gross underestimation” and presumably based on an assumption of a density of galaxies and constituent stars applied to a universe of 46.5 light years radius).  According to Kroupa, the average stellar mass sits between 0.20 and 0.38 solar masses.  A solar mass is 1.989×10³⁰kg, so that’s between 3.98×10⁵³kg and 7.56×10⁵³kg in the observable universe, as a gross underestimate.  Given that the Hubble sphere is about 2.5% the volume of an observable universe that is purported to be 46.5 light years in radius, this equates to between 1.0×10⁵²kg and 1.9×10⁵²kg.

 

But this is just stars.  What about cosmic dust?  The intergalactic medium contains about one atom per cubic metre, presumably hydrogen.  The vast majority of space is intergalactic medium, so I am going to use the whole volume of a Hubble sphere for the estimate.

 

A hydrogen atom has a mass of 1.673557×10^-27kg.  So that equates to a total mass for the intergalactic medium of 1.54987×10⁵²kg (in a Hubble sphere), for a total of identified ordinary matter between 2.55×10⁵²kg and 3.45×10⁵²kg.

 

Within a galaxy there is the interstellar medium, and astronomers estimate that, in our galaxy, the mass of that medium is equal to about 15% of the mass contained in stars.  If our galaxy is average, then this is an additional 0.15×10⁵²kg to 0.28×10⁵²kg (for a new total between 2.8×10⁵²kg and 3.7×10⁵²kg).

 

There is also a question about nebulae.  I would not count concentrations of dust (etc) such as the Horsehead Nebula as contributing to the interstellar medium, but perhaps astronomers do.  Nebulae vary greatly in size, for example the Carina Nebula has about 4,300 solar masses while the Cat’s Eye nebula is a planetary nebula and has less than one solar mass.  What the average mass of a nebula is and what is the number of them in each of the galaxies are questions to which I cannot find the answer.

 

Given that we can see only a small proportion of the Milky Way by eye (see image below, from Pablo Carlos Budassi’s image at Wikipedia), and that we can see a number of nebula from where are, my gut feeling is that there is a significant even though relatively small proportion of mass of the galaxy that resides in them.  I suspect that we can safely ignore them.

 

 

Finally, there is the supermassive black hole at the centre of galaxies (assuming that ours is typical).  We have a black hole of about 4 million solar masses.  This is about one to four parts in a hundred thousand and presumably the same could be said for other galaxies, so again, it is in the noise and can be safely ignored.

 

Nevertheless, the identified mass is in the order of half that calculated in the FUGE model.  The comment above, that the number of stars is a gross underestimate, indicates that entirety of mass in the universe could be accounted for by normal matter (stars, planets, dust), or, perhaps, there is scope for a smaller quantity of “dark matter”, in approximately the same order as ordinary matter.  If the former, then an alternative to dark matter would need to be identified.

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The other feature of the standard cosmological model that is not explained by the FUGE model is cosmic acceleration.  I have mentioned this a few times already but the evidence for cosmic acceleration is contentious.  Jacques Colin, Roya Mohayaee, Mohamed Rameez and Subir Sarkar argue that the evidence for cosmic acceleration is lacking.  The explanation, as given a little more clearly by Sabine Hossenfelder, is that the original analysis by Reiss et al. assumed that the cosmological principle applied at the scale at which they were observing supernovae – but that scale is below that at which the concordance model indicates that the cosmological principle applies.  Fundamentally, if you look closely enough, the universe is lumpy (with stellar systems, galaxies, clusters and so on), but if you zoom out and look at averages at the 200-300 megaparsec scale, then the universe is expected to be smooth.  Once you look at the evidence at the appropriate scale, the apparent acceleration goes away.

 

Remember here that cosmic acceleration only exists because of that observation of supernovae.  It doesn’t exist to bring density or Hubble parameter values into alignment with what are currently measured.  So if there were no acceleration and no dark energy, the standard cosmological model would have to be rejigged to result in the values that are reached naturally via the FUGE model (shortened periods of deceleration, redistributed periods of deceleration, reduced rates of deceleration, less inflation, and/or a new period of “standard” expansion with H=1/t).  Consider then the utility of the standard cosmological model if it can be rejigged to get any result we need.  Pretty much zero.  And if it can’t be rejigged to get the result we need.  Precisely zero.

 

It is true that the FUGE model does not explain the observations that lead to dark matter either, but if there are problems with dark matter (and there are) then we already need to look for an alternative solution.  Note that there is no problem in the FUGE model if there is a solution that, under certain circumstances, looks like there is some sort of “dark matter”, but this appearance should not necessarily be taken as meaning that there is literally an additional category of mass-energy.

 

The FUGE model explains only what you need and what you see.  There is no need for an inflaton field (which theoretically drives inflation and for which there is no experimental evidence – so we don’t see it), dark matter (the phenomenon that led to the theory of dark matter was observed in 1993, but as for actual dark matter … there is no experimental evidence – so we don’t see it) or dark energy (for which there is no experimental evidence – note that a phenomenon that leads to a proposed explanation is not evidence of the explanation being real and note also that in the link it is stated that “Currently, the only experimental evidence for dark energy is the accelerating expansion of the universe”.  So, that is not evidence – it is just the phenomenon that dark energy was proposed to explain – and if it is the only experimental evidence, then there is no experimental evidence.  Also see NASA’s comment about the complete mystery involving yet another thing that we don’t see).

 

I should note here that declarations about the balance of mass-energy in the universe (so much ordinary matter, this much dark matter and that much dark energy) are based on assumptions.  According to CERN: “researchers have been able to infer the existence of dark matter only from the gravitational effect it seems to have on visible matter”.  If there’s another mechanism, then dark matter disappears.  According to NASA: “We know how much dark energy there is because we know how it affects the universe's expansion”.  If there’s another mechanism or there is in fact no acceleration, then dark energy disappears.  And then we have just ordinary matter, at a quantity that the FUGE model produces.